Sequence And Series‌

A sequence in mathematics is a collection of objects (or events) that have been sorted sequentially so that each item occurs before or after every other member. A series is the sum of a set of terms. A series is a collection of integers having additional operations between them.

A sequence is a certain format of components in some specified order, whereas a series is the sum of the sequence's constituents. The order of the items in a sequence is fixed, but the order of elements in a series is not. A sequence is a list of integers in a certain order. Each number in the series is referred to as a word.

A number pattern is a pattern or sequence of numbers. In general, this pattern provides a similar link between all integers. To address numerical pattern issues, we must first identify the rule that is being followed in the pattern.

What is the name for each number in a sequence?

Each number in a series is referred to as a term. A position is assigned to each phrase in a sequence (first, second, third, and so on). Consider the number sequence 4, 14, 24, 34, .... Each number in the series is referred to as a word.

What is the formula for the series?

A sequence's series is the sum of the sequence up to several words. It is frequently abbreviated as Sn. So, if the sequence is 2, 4, 6, 8, 10, ..., the sum of 4 terms equals S4 = 2 + 4 + 6 + 8 = 20.

What is the most well-known sequence?

The Fibonacci Sequence is probably the most well-known of all mathematical sequences. It goes: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.

What is the infinite series formula?

While calculating the sum of a GP, we discover the total converges to a value, although the series has infinite terms. Sum = a/(1-r) is the formula for the infinite series.

What is the sequence's nth term?

An arithmetic sequence's nth term is provided by a = a + (n – 1)d. The integer d is known as the common difference because any two successive terms of an arithmetic series differ by d, and it can be determined by subtracting any two terms a and an+1.

What is 1 + 2 + 3 + 4 + 5 + … + ∞?

The series is popularly called the Ramanujan Summation which goes after the name of a famous Indian mathematician, Srinivasa Ramanujan. It asserts that if we add all the natural numbers, 1, 2, 3, 4, and so on, all the way to infinity, it equals -1/12.

What exactly are infinite sequences and examples?

An infinite sequence is a set of discrete object numbers that can be paired off one-to-one with the set of positive integers 1, 2, 3,...

Infinite sequences include N = (0, 1, 2, 3, ...) and S = (1, 1/2, 1/4, 1/8,...).

What are the implications of sequence and series daily?

Sequences and series play a vital part in many facets of our life. They assist us in deciding by allowing us to forecast, assess, and monitor the outcome of a situation or occurrence.

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Introduction to p-Block elements

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Handpicking

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Electrode

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Frenkel Defect

Deforestation

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Gattermann – Koch Reaction Mechanism

Electronegativity

Industrial Waste: Types

Ethylene

Charge to Mass Ratio of an Electron

Fehling Solution

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Second Order Reaction

Etard Reaction

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Preparation of Acetanilide

Metallic Minerals and Non-Metallic Minerals

Ferric Chloride Henry's Law Preparation of Mohr's salt

Schottky Defect

Claisen rearrangement

Calcium sulphate

Sodium carbonate

Rubber

Ethyl acetate

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Resorcinol

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States of Matter

Boric Acid

Types of Minerals

Finkelstein Reaction

Electronegativity Chart

Difference between Solid, Liquid and Gas in tabular form

Aromaticity

Drawbacks of Rutherford's Atomic Model

Thermosetting Polymers

Preparation of Alkanes

Examples of Bases

Suzuki Coupling Reaction

Standard Electrode Potential

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Reducing Agent

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Hard Water and Soft Water

Organometallic compounds

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Slaked Lime

Borax

Tetravalency of Carbon

Boyle's Law

Ellingham Diagram

Crystal Defects : Point Defects

HVZ Reaction (Hell-Volhard-Zelinsky Reaction)

Classification of Drugs

Preparation of Sulfuric Acid

Lucas test

Xenon Difluoride

Bravais Lattice

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Elimination Reaction

preparation of polythene, Teflon and polyacrylonitrile

Difference between cations and anions

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Fructose

Azeotropes

Lewis Acid and Base

Emulsification

Dielectric properties of solids

Zwitterion

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Oxidation and Reduction

Electrophilic Substitution Reaction

Suspensions

Aromatic Compounds

Ores and Minerals

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Wittig Reaction

Difference between evaporation and boiling

Intensive And Extensive Properties Of Matter

Electronic Configuration of Group 16 Elements

Difference Between Elements and Atoms

Sodium Oxide

Gypsum

Difference Between Alloy and Composite

Chemical Equations

Thorium

Lead Acid Battery

Isotopes of Hydrogen

Figure Rules

Electrophilic Addition Reactions Of Alkenes

Isothermal Expansion of an Ideal Gas

Potassium Chloride - KCl

Aluminum Oxide

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Test for Phenolic group

To prepare colloidal solution of starch

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Pi Bonds

Potassium Chlorate

Schmidt Reaction

High density Polyethylene

Huckel's Rule

Discovery of Proton

Aluminium Ore: Extraction of Aluminium

Benzene Hexachloride

Caustic Potash or Potasium Hydroxide

Electromagnetic Radiation - Wave Nature

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Butane

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Scandium

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Copper

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Lipids

Living Things

Macromolecule Meiosis 1 Stages and Process Mendelian Disorders Microbodies Modern Synthetic Theory of Evolution Monera Nephron Function Renal Tubules Nuclear Membrane Nucleolus Nucleus Our Environment Parasitism Parts of Plants Passive Transport Plant Cell Plant Kingdom Plantae Plant Respiration Plants Plastids Protista Red Data Book Reproductive System of Earthworm Ribosomes Scientific Names of Animals and Plants Seed germination Sensory Perception Snail Skeletal System Spermatogenesis Structure Of Eye Taxonomic Hierarchy Taxonomy Algae Thallophyte

Types of Soil

Vacuoles What Is Adaptation Agricultural Practices Animal Kingdom Alimentary Canal Coelenterata Conservation of Forest and Wildlife Difference between Endosmosis and Exosmosis Difference between Afforestation and Deforestation Difference between Algae and Fungi Difference between Cereals and Pulses Difference Between Fragmentation and Regeneration Difference Between Neurosis and Psychosis Difference Between Nucleotide and Nucleoside

Difference Between Sea and Ocean

Difference Between Turtles and Tortoises

Difference Between Wildlife Sanctuary and National Park

Modes of Plant Reproduction

Ecological Pyramid and Its Types

Double Fertilization in Angiosperms

Ecosystem Enzymes

Fertilisation in Plants

Five Kingdoms Classification

Ganongs Potometer

Health and Hygiene

Herbivores and Carnivores

Heterotrophic Nutrition Human Digestive System

Vertebrates and Invertebrates

Morphology of Leaves

Modifications of Root

Phylum Aschelminthes

Diffusion

Osmosis

Prokaryotic Cells

Reproduction

Flora And Fauna

Overview of Food Chain

Difference Between Rabi And Kharif Crops

Vegetative Propagation Angiosperms Characteristics Soil Profile

Types of Pollution

Human Excretory System Sense Organs Rainwater Harvesting

Prokaryotic And Eukaryotic Cells

Living And Non Living Things

The Nucleus

Irrigation

Endoplasmic Reticulum

Between Data And Information

Mitochondria

Nitrogen Cycle

Diagram of Animal Cell

Meristematic Tissue

Law of Segregation Law of Dominance

Eukaryotic Cells

Sources Animal Plant Products

Photosynthesis Respiration Ozone Layer Depletion Kingdom Fungi Aerobic Anaerobic Respiration Cell Organelles Peristalsis Bacteria Oogenesis

Leaves Morphology Types Modification

Mitosis and Meiosis

How Do Organisms Reproduce

Diagram of Stomata

Monohybrid Cross Inheritance One Gene Mechanism of Breathing

Soil Erosion

Plasmolysis

Urine Formation Osmoregulation

Porifera

Flagella

Amoeba

Aerobic Respiration

Pteridophyta

Arteries And Veins Difference

Reflex Action

Stomata

Cell Wall

Diagram of Neuron

A Guide To Composition And Function Of Lymph

Difference Between Ligaments And Tendons

Insectivorous Plants

Nutrition Modes Living Organisms

Mendel Laws Of Inheritance

Nutrition In Amoeba

Calorific Value

Air Pollution Control

Fertilization In Plants

Binary Fission

Omnivores

Saprophytes

Asexual Reproduction

Deficiency Diseases

Light Reaction Vs Dark Reaction

Global Warming

Wildlife Sanctuary

Viviparous Oviparous Embryo Development

Food Preservation Methods Food Poisoning

Crops

Biofertilizers

Biodiversity Conservation

Difference Between Endocrine And Exocrine Glands

Greenhouse Effect Gases

Diagram Of Digestive System

Crop Production And Management

Types Of Pollination

Introduction and Characteristics of Living Beings Meristematic Cells Taxonomical Aids _Flora, Manual, Monograph And Catalogues Types of leaves structure of skeletal muscle spirometry human respiratory system herbarium dinoflagellates general characters and structure of leaf halophiles and their features Exchange of Gases Simple Permanent tissue Morphology of root and its types Complex permanent tissues Regions of Root History of classification and its need Breathing And Exchange Of Gases Transport of Gases Regulation of Respiration Disorders of Respiratory System Interaction of Haemoglobin with Other Gases Amniocentesis Anatomy of flowering plants ASSISTED REPRODUCTIVE TECHNOLOGIES (ARTs) Meristematic Cells Phloems Population explosion Reproductive Health RCH (Reproductive and Child Health Care) Medical termination of Pregnancy (MTP) Plant kingdom Biological Systems of Classification & Branches of Taxonomy Pteridophytes Gymnosperms Angiosperms Life cycle Patterns Anatomy of Roots Contraceptives Anatomy of stem Algae Bryophytes Tissues and its types STDs (Sexually Transmitted Diseases) Cell - The Basic Unit of Life & its Historical background Cell theory and its modification An Overview of Cell Secondary growth in dicot stem Tissue system and types Prokaryotic (Bacterial) cell Ribosomes Eukaryotic cell Cell: The basic unit of life Cytoskeleton Centrosome and Centriole Cilia and flagella Nucleus Chromosomes Evolution Movement and Locomotion Human Reproduction Absorption and Translocation of Solutes Soil as a reservoir of Essential Elements LOCOMOTION AND MOVEMENT Mechanism of Muscle Contraction Morphology in Flowering Plants Contractile proteins Muscular System Thyroid Puberty Hormones Origin of Universe Hypothalamus Cell wall Mitochondria Special Chromosomes Microbodies Introduction, Hydroponics and the study of mineral requirements of the plants Criteria of essentiality and Categorisation of Essential elements Deficiency symptoms of essential elements and toxicity The Stem The Root Cytoplasm and cell membrane Mineral Nutrition Disorders Related To Reproductive System Phylum Ctenophora Role of Macronutrients Role of Micronutrients Phylum - Coelenterata / Cnidaria Reptilia Aves Mammalia Anatomy of the leaf Animal kingdom Phylum Annelida Phylum Mollusca Phylum Echinodermata Vertebrata Chordates Disorders of circulatory system Abiotic Factors Male Reproductive System Kingdom Animalia Responses to Abiotic Factors Female Reproductive System Mammary Glands Pregnancy and Embryonic Development Cell Cancer Disorders of the Digestive System Infertility Morphology of Cockroach Blood and Plasma Alternation of Generations and Classification Predation Phaeophyceae and Rhodophyceae Phylum Coelenterata Phylum Porifera Phylum Platyhelminthes Chromosomal Disorders Competition Taxonomic Aids Alternation of generation in Pteridophytes Disorders of muscular and skeletal system General Characteristics of Living Digestive Glands Stomach Testis Buccal cavity Seed Common Diseases in Humans Permanent Tissue Permanent Tissues Xylem Pteridophytes Characteristics Parasitism and Commensalism Water Pollution and Its Control Differentiation, Dedifferentiation and Redifferentiation Organism and its Environment Carbohydrates Greenhouse Effect Gases Amino Acids Dynamic State of Body Constituents Photosynthesis Chloroplast Features of Living Beings Blood Group Lipids Kingdom Protista dense connective tissue connective tissue cartilage connective tissue blood plant cell viruses the stem Connective Tissue Bone Viroids Prions Lichens Animal cell Prokaryotic Cell Taxonomic Aids Herbarium and Museum Sphygmomanometer and ECG Population Attributes Noise pollution Diaphragm Parts of a Plant Photoperiodism Poultry Farming Nucleic Acids Cell Cycle Principles of Biotechnology Antibiotics IVF Glands Kranz Anatomy Sexual Reproduction in Plants Cytokinin Plant Development Biofertilizers Photorespiration Auxin Nutrient Cycling Types of Flowers Taxonomic Hierarchy and Categories Epidermal Tissue System Calyx and Corolla Ethylene Fertilization and Implantation Types of Fruits Inflorescence Types of Growth Macronutrients Family Liliaceae ETC and Oxidative Phosphorylation Classification of Wood Ground Tissue System Secondary Growth in Stem Plant Vascular System Electron Transport System Transpiration Difference Between Types of Cells Ovary Structure Birth Control Epithelial Tissue Endomembrane System Cell Envelopes and Cell Membrane Muscle Types Axial Skeleton Acquired Immunity Lung Volumes and Capacities Suspension and Migration Prokaryotic Cells

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